Only I don't have a blender. Think it would be just as good if I used a hand mixer to puree it?

Hand mixer is fine, the final texture of the soup will not be as smooth. Might even be a little lumpy. Won't affect the taste though and some people like their soup a little lumpy. If I make potato soup for company I have to leave it lumpy for one of my friends.

If I was going to use a hand mixer, I would do things a little differently however.

1) Let the pumpkin shimmer a little longer.
2) Use a ricer (device to make mash potatoes) or a masher to break up the pumpkin first.
3) Once it is all broken down, let it shimmer a little again (maybe 5 minutes) before mixing.
4) Take it off the heat and make sure the sides of the pot is high enough so that you don't get bits of soup everywhere.

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